Question

A beaker of mass 1.2 kg containing 2.3 kg of water rests on a scale. A 3.1 kg block of a metallic alloy of density 4700 kg/m3 is sus- pended from a spring scale and is submerged in the water of density 1000 kg/m3. What does the hanging scale read? The acceleration of gravity is 9.8 m/s2 . What does the lower scale read?

Answer 1

block mass m=3.1 kg,

density ?=4700kg/m³

Volume of block V=m/d

=3.1/4700

= 0.659x10^-3m³

Mass of water displaced by the block

M_w =V*?_w

= 0.659*10^-3*1000

= 0.659kg

The block will get a push from the water equal to the weightof the water displaced by the block, or the effective weight of theblock is reduced by the same a mount:

Weff = (m-M_w)*g

= (3.1-0.659)9.8

= 23.92 N (this isthe reading on the hanging scale)

The bottom scale will gain by the same amount (0.659kg).

We know that...

Totalweight on the bottom scale:

W_bot = (1.2+2.3+0.659)*9.8

=  40.76N(reading on bottom scale)